基于通讯数据的社群聚类数学研究

Mathematical research on community clustering based on communication data

运用PageRank算法、SimRank算法、聚类分析和概率统计估计法等对实际通讯数据的社群分类问题进行了聚类判别和分析。运用PageRank算法和SimRank算法分别对无向图和有向图分析发现:无向图中点1为一类,2、3、4为一类,5、6为一类,有向图中点2、4之间和点3、5之间的相似度高,对个体进行了初步识别,实现了分群。基于对通讯数据的分析得出节点2、3、5、10为一类,其他节点为一类,实现了个体的分群,并得出最佳信息投放方案为只投放节点2、3。通过考虑时间和通话频率对之前问题结果的影响得出最优的投放方式应选择节点2、3在下午时段进行。

For question B of the 10th Central China University Students Mathematical Modeling Invitational Contest in 2017,this paper systematically and completely introduces and applies PageRank algorithm,SimRank algorithm,clustering analysis and probability statistical estimation methods to make clustering analysis on the community classification of actual communication data.PageRank algorithm and SimRank algorithm are used to analyze undirected graph and directed graph respectively.Points 1 in undirected graph is a class,2,3,4 in undirected graph is a class,and 5,6 in undirected graph is a class.Points 2,4 and 3,5 in directed graph have high similarity.Individuals are preliminarily identified and clustering is realized.Based on the analysis of communication data,it is concluded that nodes 2,3,5 and 10 are in one category,and other nodes are in one category.Individual clustering is realized,and the best information delivery scheme is only to put nodes 2 and 3.Considering the influence of time and call frequency on the results of previous problems,it is concluded that the optimal mode of delivery should be node 2 and 3 in the afternoon.